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How
the Wayfinder Determines Latitude
(Revised:
January 8, 2001, based on questions and comments from Ilyan Thomas,
Carmarthen, Wales, UK.)
Latitude-Height of
Stars Crossing the Meridian
Latitude is the
distance on the earth's surface from the equator. It is given in
degrees north or south of the equator (One degree of latitude equals
60 nautical miles; each degree contains sixty minutes; one latitude
minute equals one nautical mile.)
One strategy of
locating an island without navigational instruments is called
lattitude sailing. It involves sailing to the latitude of an island,
preferrably upwind, then searching for the island along that
latitude. For this strategy to work, the navigator must be able to
tell when he is at the latitude of the island. The navigator can
make a rough estimate from his dead reckoning, but there are more
precise methods to determine latitude without instruments.
The North Star /
Hokupa'a
North of the equator,
the altitude of the relatively fixed star Hokupa'a (Polaris, the
North Star) is approximately equal to the latitude of the observer.
(Hokupa'a is actually 44' from the celestial north pole and
inscribes a 1.5° circle around it.)
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At the equator (0 °
latitude), Hokupa'a is about at the horizon (0 ° altitude);
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at 10 ° N latitude,
Hokupa'a is about 10 ° above the horizon;
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at 20 ° N
latitude-within the latitudes of Hawai'i-Hokupa'a is about 20 °
above the horizon, and so on.
The altitude of the
star can be measured using the hand stretched out in front of the
eyes, with shoulders squared. Different configurations of the hand
( e.g., a fist, a span, two fingers, three fingers, etc.) can be
calibrated to distances (degrees) in the sky.
Meridian Pairs
Stars crossing the
meridian can also be used to estimate latitude. At given
latitudes, a star crosses the meridian at a certain altitude. If
the navigator knows the altitude of the meridian crossing of a
star at a particular latitude, and he can tell when the star is
crossing the meridian, he can estimate his latitude by measuring
the altitude with his hand. To know when a star is crossing the
meridian, the navigator uses meridian pairs--stars which cross the
meridian togther. When the pair is perpendicular to the horizon,
the stars are crossing the meridian. (The meridian is an imaginary
line on the celestial sphere passing through the north and south
celestial poles and the zenith, the point directly above the
observer's head. The closer a star is to the horizon, the more
accurately its altitude can be measured without instruments.
However, stars that cross the meridian too close to the horizon,
1-3 ° from it, often cannot be seen because of clouds, dust, sea
spray, etc.)
At the equator, the
altitude of a star as it crosses the meridian is equal to 90 °
minus the star's declination. (The declination of a star gives the
position of a star on the celestial sphere, measured in degrees
away from the celestial equator, an imaginary circle that passes
through due east and due west.
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A star on the
celestial equator has a declination of 0°;
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a star 30° north of
the celestial equator has a declination of 30°, and so on.
(The declinations of
stars are published in astronomical handbooks.)
The Southern Cross
/ Hanaiakamalama: One meridian pair is the top and bottom
stars in the Southern Cross, Gacrux (Kaulia) and Acrux (Ka Mole
Honua).
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At the equator,
Kaulia (Gacrux) crosses the meridian 33 ° above the horizon due
south: 90 ° - 57 ° (dec. of Kaulia) = 33 °.
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At the equator, Ka
Mole Honua (Acrux) crosses the meridian 27 ° above the horizon due
south: 90 ° - 63 ° (dec. of Kaulia) = 27 °.
As the observer moves
north of the equator, these two stars will cross the meridian at
lower and lower altitudes above the south celestial pole; the
observer can substact his latitude from the altitude of the star
crossing the meridian at the equator to get the altitude at which
the star crosses the meridian at his new latitude.
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At 10 ° N, Kaulia
(Gacrux) crosses the meridian 23 ° above the horizon due south: 33
° - 10 ° (lat. N of the equator) = 23 °.
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At 10 ° N, Ka Mole
Honua (Acrux) crosses the meridian 17 ° above the horizon due
south: 27 ° - 10 ° (lat. N of the equator) = 17 °.
As the observer moves
south of the equator, the two stars in the Southern Cross would
cross the meridian at a higher and higher altitude; the observer
adds his latitude south of the equator to the altitude of the star
crossing the meridian at the equator to get the altitude at which
the star crosses the meridian at his new latitude.
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At 10 ° S, Kaulia
will be 43 ° high as it crosses the meridian: 33 ° + 10 ° (lat. S
of equator) = 43 °.
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At 10 ° S, Ka Mole
Honua will be 37 ° high as it crosses the meridian: 27 ° + 10 °
(lat. S of equator) = 37°.
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At 21 ° N (about
mid-latitude of Hawai'i), Kaulia (Gacrux) crosses the meridian at
12 ° above the horizon: 33° - 21° = 12°
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At 21 ° N, Ka Mole
Honua (Acrux) crosses the meridian 6 ° above the horizon due
south: 27° - 21° = 6°
Click here for a Diagram of the Southern
Cross at the Meridian in Hawai'i.
The fact that the
distance between Ka Mole Honua and the horizon, and Kaulia and Ka
Mole Honua are equal (6 °) is an additional clue to the latitude
of Hawai'i.
As the sun passes
through the zodiac over the course of the year, the stars in the
portion of the sky in which the sun is located are not visible. So
those stars would not be available for determining latitude at
that time of the year. The navigator uses meridian pairs that are
visible after sunset and before dawn at the time of the voyage.
Voyages are planned for times of the year when the weather and
winds are optimum and also when certain meridian pairs are
visible. For example, when sailing to Hawai'i from the South
Pacific, the navigator wants to have the Southern Cross crossing
the meridian in the night sky for determining when the canoe has
reached the latitude of Hawai'i. Click here for
lists and diagrams of meridian pairs used
during the voyage to Rapanui (1999-2000). The Southern
Cross was visible crossing the meridian in the predawn sky as
Hokule'a returned to Hawai'i in February, 2000.
Latitude-Rising
and Setting Pairs
Pairs of stars that
rise or set at the same time can also be clues to latitude. Pairs
rise and set together only at specific latitudes. For example,
when 'A'a (Sirius) and Nana-hope (Pollux) set together, the
observer is at the latitude of Tahiti, or 17 ° S. As the observer
moves north or south of that latitude, one or the other star will
begin to rise or set before or after the other star. It is easier
to use setting rather than rising pairs of stars to determine
latitude, because the observer can watch the pair as it approaches
the horizon instead of trying to anticipate their appearance.
Zenith Stars
At a given latitude,
only certain stars will pass through the zenith, the imaginary
point in the sky directly overhead. The most conspicuous (i.e.
brightest) of these stars is called the zenith star of that
latitude. The zenith star of Hawai'i is Hokule'a (Arcturus); the
zenith star of Tahiti is 'A'a (Sirius). The declination of the
zenith star is equal to the latitude it is associated with. Thus
the declination of Hokule'a (Arcturus) is 19 ° N; the latitude of
South Point on the Big Island of Hawai'i is about 19 ° N; the
declination of 'A'a (Sirius) is 17 ° S; the latitude of Tahiti is
17 ° S.
If the navigator
knows the zenith stars of different latitudes, he can tell what
latitude he is at by observing what star passes directly overhead
at night. However, while the observer can make a rough estimate,
it is difficult to tell when a star is passing directly overhead
on a canoe that is pitching, rolling, or corkscrewing along. The
observation is not as precise for determining altitude as the
other methods: (1) measuring altitude of Hokupa'a north of the
equator; (2) measuring the altitude of stars as they cross the
meridian; or (3) watching for pairs of stars that rise or set
together.
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